TheWtransformation, a matrix transformation, is developed and applied for the mixed analysis of variance model to compute maximum likelihood estimates of the variance components and fixed parameters. This transformation not only eliminates the need for the explicit computation of then×ninverse matrix H−lbut permits handling the iterative calculations such that they do not depend uponn(the number of observations) in any way. Although not wedded to a particular numerical method, theWtransformation is implemented in conjunction with a modified Newton-Raphson method in which variance components are restricted to being non-negative.